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Majority vs. Approximate Linear Sum and Average-Case Complexity Below NC¹

Lijie Chen, Zhenjian Lu, Xin Lyu, Igor C. Oliveira, Nikhil Bansal, Emanuela Merelli, James Worrell
2021
Crucial to these results is the use of non-black-box hardness amplification techniques and the interplay between Majority (MAJ) and Approximate Linear Sum (SUM̃) gates.  ...  We develop a general framework that characterizes strong average-case lower bounds against circuit classes 𝒞 contained in NC¹, such as AC⁰[⊕] and ACC⁰.  ...  A crucial ingredient in our proofs is the interplay between Majority (MAJ) and Approximate Linear Sum ( SUM) gates.  ... 
doi:10.4230/lipics.icalp.2021.51 fatcat:mdtczu5akfh67fodxdvwe3w2bq

Mean-field/PDF numerical approach for polydispersed turbulent two-phase flows

E. Peirano, S. Chibbaro, J. Pozorski, J.-P. Minier
2006 Progress in Energy and Combustion Science  
of the averaging and projection operators, the time integration of the SDEs (weak numerical schemes consistent with all asymptotic cases), and the computation of the source terms.  ...  , i.e. the consistency of the system of SDEs in asymptotic cases.  ...  Fig. 2 . 2 CIC scheme used to compute cell averages for (a) particle density and (b) a linear function attached to particles (the linear function is defined by its slope DF and F 0 which is the value of  ... 
doi:10.1016/j.pecs.2005.07.002 fatcat:tegydbagzne4ppm33todtckxmy

Approximation and Interpolation [chapter]

Walter Gautschi
2011 Numerical Analysis  
He made also notable contributions to approximation theory in the complex plane. 8 Sergei Natanovič Bernštein (1880-1968) made major contributions to polynomial approximation, continuing in the tradition  ...  In the case of the least squares problem, however, we admit general linear spaceŝ of approximants, and also in the case of the interpolation problem, we include polynomial splines in addition to straight  ...  n .x/ D Q n kD0 .x k/, let M n be the largest, and m n the smallest, relative maximum of j ! n .x/j. For n D 5 W 5 W 30 calculate M n , m n , and M n =m n , using Newton's method (cf.  ... 
doi:10.1007/978-0-8176-8259-0_2 fatcat:jjnf7buogrhijg3zuj6q5pohea

Two-exponential models of gene expression patterns for noisy experimental data [article]

Theodore Alexandrov, Nina Golyandina, David Holloway, Alex Shlemov,, Alexander Spirov
2017 arXiv   pre-print
This approach: 1) has natural, biologically relevant parameters; and 2) is invariant to linear transformations of the data which can arise due to variation in experimental conditions (e.g. microscope settings  ...  Motivation: Spatial pattern formation of the primary anterior-posterior morphogenetic gradient of the transcription factor Bicoid (Bcd) has been studied experimentally and computationally for many years  ...  NIH grant R01-GM072022 and the Russian Foundation for Basic Research grants 15-04-06480 and 16-04-00821.  ... 
arXiv:1704.00351v1 fatcat:csdskjr43rhkbepezc7tc45kka

Influences of landscape characteristics and historical barriers on the population genetic structure in the endangered sand-dune subterranean rodent Ctenomys australis

Ailin Austrich, Matías S. Mora, Fernando J. Mapelli, Alberto Fameli, Marcelo J. Kittlein
2020 Genetica  
Understanding the processes and patterns of local adaptation and migration involves an exhaustive knowledge of how landscape features and population distances shape the genetic variation at the geographical  ...  We use 13 microsatellite loci in a total of 194 individuals from 13 sampling sites to assess the dispersal patterns and population structure in the complete geographic range of this endemic species.  ...  To these persons and institutions, we express our deep gratitude.  ... 
doi:10.1007/s10709-020-00096-1 pmid:32451787 fatcat:hgohyev7snft3fsvmxvtjq3awa

Phylogeography and Ecological Niche Modeling Reveal Reduced Genetic Diversity and Colonization Patterns of Skunk Cabbage (Symplocarpus foetidus; Araceae) From Glacial Refugia in Eastern North America

Seon-Hee Kim, Myong-Suk Cho, Pan Li, Seung-Chul Kim
2018 Frontiers in Plant Science  
ACKNOWLEDGMENTS The authors thank Hee-Young Gil, Jun Wen, Tim McDowell, Sue Lutz, Joon Seon Lee, Chih-Chieh Yu, Shen-Yi Wang, Zhe-Chen Qi, and Jenny Xiang for their assistance during fieldwork, and John  ...  We would also like to thank the three referees whose helpful comments and suggestions greatly improved the manuscript.  ...  In the case of the herbaceous Smilax herbacea complex (Li et al., 2013) , nucleotide diversity and haplotype diversity were slightly higher in Midwestern populations than in East Coast populations.  ... 
doi:10.3389/fpls.2018.00648 pmid:29872442 pmcid:PMC5972301 fatcat:26g6utyc2begjhhsoudbgscchq

Diffusion Equations [chapter]

Svein Linge, Hans Petter Langtangen
2017 Finite Difference Computing with PDEs  
The exposition is, as usual in this book, very basic and focuses on the basic ideas and how to implement.  ...  And of more importance, since the solution u of the diffusion equation is very smooth and changes slowly, small time steps are not convenient and not required by accuracy as the diffusion process converges  ...  Iterations Let u nC1;r i;j be the approximation to u nC1 i;j in iteration r, for all relevant i and j indices.  ... 
doi:10.1007/978-3-319-55456-3_3 fatcat:ia6avvcx65bcxeovtkpv6gefbe

Data Enrichment [chapter]

2017 Encyclopedia of Machine Learning and Data Mining  
If the attribute is numerical, the tree may be more complex.  ...  Data preparation is typically an iterative process of manipulating raw data, which is often unstructured and messy, into a more structured and useful form that is ready for further analysis.  ...  Each technique has its own purpose and dependency on the nature of data. Some of the major transformations are discussed below.  ... 
doi:10.1007/978-1-4899-7687-1_979 fatcat:v22x3o5iuzaa5ghwx5fvqztpg4

General theory of carrier lifetime in semiconductors with multiple localized states

Didier Debuf
2004 Journal of Applied Physics  
,m without an approximation at a given temperature for an excess carrier concentration below nondegenerate doping, arbitrary uniform doping concentration N A,D , defect level concentration N k , cross  ...  section nk,pk , and energy level E k .  ...  Since each monoexponential term is the re-a) sponse to a linear system, the solution is the sum of the responses of an infinite number of linear systems.  ... 
doi:10.1063/1.1805192 fatcat:323azquwmrhflfxn72jjsqxup4

Potential Novel Thioether-Amide or Guanidine-Linker Class of SARS-CoV-2 Virus RNA-Dependent RNA Polymerase Inhibitors Identified by High-Throughput Virtual Screening Coupled to Free-Energy Calculations

Marko Jukič, Dušanka Janežič, Urban Bren
2021 International Journal of Molecular Sciences  
with Linear Interaction Energy calculations.  ...  available as well as suitable for further biological evaluation and mode of action studies.  ...  We thank OpenEye for the academic licensing of their software and their help and support. We thank Elmar Krieger for his support and help.  ... 
doi:10.3390/ijms222011143 pmid:34681802 fatcat:wubouw6uefcqxgkr6kg4fhtkia

Symbolic Dynamics, Poincaré Plot Analysis and Compression Entropy Estimate Complexity in Biological Time Series [chapter]

Steffen Schulz, Andreas Voss
2017 Complexity and Nonlinearity in Cardiovascular Signals  
In this chapter prominent complexity methods of non-linear dynamics as symbolic dynamics, Poincaré plot analyses, and compression entropy are introduced and their algorithmic implementations and application  ...  Methods from nonlinear dynamics have shown new insights into alterations of the cardiovascular system under various physiological and pathological conditions, and thus providing additional prognostic information  ...  linear and further successful non-linear approaches.  ... 
doi:10.1007/978-3-319-58709-7_2 fatcat:xm6vtqug7rasxkhgys6jd4lauu

Distribution of Classification Margins: Are All Data Equal? [article]

Andrzej Banburski, Fernanda De La Torre, Nishka Pant, Ishana Shastri, Tomaso Poggio
2021 arXiv   pre-print
in the presence of both batch normalization and weight decay.  ...  We motivate theoretically and show empirically that the area under the curve of the margin distribution on the training set is in fact a good measure of generalization.  ...  Acknowledgments This material is based upon work supported by the Center for Minds, Brains and Machines (CBMM), funded by NSF STC award CCF-1231216.  ... 
arXiv:2107.10199v1 fatcat:eol6dpd2fzha5myjhr2yskbthu

Pion production in neutrino interactions with nuclei

T. Leitner, O. Lalakulich, O. Buss, U. Mosel, L. Alvarez-Ruso
2009 arXiv   pre-print
Neutrino-induced pion production on nuclear targets is the major inelastic channel in all present-day neutrino-oscillation experiments.  ...  While this duality holds quite well for nucleon targets, for nuclear targets the average resonance contributions to the structure function F_2 are always lower than the DIS values.  ...  In this case even more events with pions in the final state appear as CCQE-like because these pions are below threshold and thus not detected.  ... 
arXiv:0910.2835v1 fatcat:4hshpxqtdvdklk3anakmcsd5uq

Effect of overhang on wind-driven rain wetting of facades on a mid-rise building: Field measurements

Hua Ge, Vincent Chiu, Ted Stathopoulos
2017 Building and Environment  
The relationship between overhang effectiveness and distance from the roofline is quasi-linear with smaller gradient for the larger overhang.  ...  and a total of 31 WDR gauges measuring WDR on building facades.  ...  the Faculty of Engineering and Computer Science of  ... 
doi:10.1016/j.buildenv.2017.03.034 fatcat:dmtvvqawlzbllovvpygtzl5f64

Quantum Computation Beyond the Circuit Model [article]

Stephen P. Jordan
2008 arXiv   pre-print
improving the intrinsic fault tolerance of adiabatic quantum computers using quantum error detecting codes, a proof that a certain problem of estimating Jones polynomials is complete for the one clean qubit complexity  ...  It provides both a framework for formulating quantum algorithms and an architecture for the physical construction of quantum computers.  ...  By following this chain we will reach the major open questions about complexity classes and their relations to one another. The big-O notation is defined as follows. Definition 1.  ... 
arXiv:0809.2307v1 fatcat:2j7vl7hmprge7oqyalfoipboum
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